UNIT 2.3 • Data Analysis
ACCURACY & PRECISION
Idea 1: Measurements (3.25 cm) ___________________________________________ numbers (3.14159265).
Measurements represent an action by someone with ______________________________
Measurements have built-in uncertainty; no measurement ______________________
Measurements have ____________________
Idea 2: The uncertainty in a measurement needs to be communicated.
Definitions:
accuracy – how close a measurement is to _______________________________
precision – how close a measurement is to _______________________________
Precision versus Accuracy:
Look at each target below and decide whether the situation is accurate, precise, both, or neither:
(Note: it is “accepted” that the bull’s eye is the place everyone aims for.)
Accurate?: Yes / No
Precise?: Yes / No
Accurate?: Yes / No
Precise?: Yes / No
Accurate?: Yes / No
Precise?: Yes / No
_________________________________ measures Precision
___________________________________ measures Accuracy
Error range = Average ± range of values
Precision Problems:
Several lab groups measure the density of aluminum. Here is their data:
Team 1
Team 2
Team 3
Team 4
Team 5
2.65 g/cm3
2.75 g/cm3
2.80 g/cm3
2.77 g/cm3
2.60 g/cm3
Team 6
2.65 g/cm3
Team 7
2.68 g/cm3
What is the average density? ________g/cm3
Subtract the highest value from the lowest value: _________
Divide this number by 2: _______
The precision of the measurement can be shown as ________±_____ g/cm3.
This is called __________
CHEMISTRY NOTES – DATA AND MEASUREMENTS
Team 1
Team 2
3
2.65 g/cm
Team 3
3
2.73 g/cm
Team 4
3
2.71 g/cm
Team 5
3
2.74 g/cm
Team 6
3
2.65 g/cm
Team 7
3
2.64 g/cm
3
2.78 g/cm
Find the error range for the new samples above.
Is this more precise, less precise, or the same precision as the previous set of data?
Accuracy Problems:
% error =
actual value − experimental value
actual value
x 100
1. Working in the laboratory, a student find the density of a piece of pure aluminum to be 2.85
g/cm3. The accepted value for the density of aluminum is 2.699 g/cm3. What is the student's percent
error?
2. A student experimentally determines the specific heat of water to be 4.29 J/g x Co. He then looks
up the specific heat of water on a reference table and finds that it is 4.18 J/g x Co. What is the percent
error?
3. A student takes an object with an accepted mass of 200.00 grams and masses it on her own
balance. She records the mass of the object as 196.5 g. What is her percent error?
4.
Often, with accuracy we are concentrating on one measurement. However,
we can also look at a collection of measurements and simply take the average.
Does this target represent someone who is accurate? _____ Precise? ____
CHEMISTRY NOTES – DATA AND MEASUREMENTS
TEACHER VERSION
Chapter 2 • Data Analysis
ACCURACY & PRECISION
Idea 1: Measurements (3.25 cm) are different than other numbers (3.14159265).
Measurements represent an action by someone with some measuring instrument.
Measurements have built-in uncertainty; no measurement is exact.
Measurements have units.
Idea 2: The uncertainty in a measurement needs to be communicated.
Definitions:
accuracy – how close a measurement is to the right answer (correctness)
precision – how close a measurement is to each other (consistency)
Precision versus Accuracy:
Look at each target below and decide whether the situation is accurate, precise, both, or neither:
(Note: it is “accepted” that the bull’s eye is the place everyone aims for.)
Accurate?: Yes / No
Precise?: Yes / No
Error Range measures Precision
Percent Error measures Accuracy
Accurate?: Yes / No
Precise?: Yes / No
Accurate?: Yes / No
Precise?: Yes / No
Error range = Average ± range of values
Precision Problems:
Several lab groups measure the density of aluminum. Here is their data:
Team 1
Team 2
Team 3
Team 4
Team 5
3
3
3
3
2.65 g/cm
2.75 g/cm
2.80 g/cm
2.77 g/cm
2.60 g/cm3
Team 6
2.65 g/cm3
Team 7
2.68 g/cm3
What is the average density? 2.70 g/cm3
Subtract the highest value from the lowest value: 2.80-2.60=0.20
Divide this number by 2: 0.20/2 = 0.10 g/cm3
This is the range of values
The precision of the measurement can be shown as 2.70 ± 0.10 g/cm3
This is called Error Range
CHEMISTRY NOTES – DATA AND MEASUREMENTS
Team 1
Team 2
3
2.65 g/cm
Team 3
3
2.73 g/cm
Team 4
3
Team 5
3
2.71 g/cm
2.74 g/cm
Team 6
3
2.65 g/cm
Team 7
3
2.64 g/cm
3
2.78 g/cm
Find the error range for the new samples above.
2.70 ± 0.07 g/cm3
Is this more precise, less precise, or the same precision as the previous set of data?
More precise, because the range of values is smaller than above
For Percent Error:
Actual value is the “correct” measurement. It usually comes from a reference book, textbook, the internet, or a known standard.
Experimental value is what is measured in the experiment, either by the student or by a scientist
Accuracy Problems:
% error =
|
actual value − experimental value
| x 100
actual value
1. Working in the laboratory, a student find the density of a piece of pure aluminum to be 2.85
g/cm3. The accepted value for the density of aluminum is 2.699 g/cm3. What is the student's
percent error?
Accepted = actual = 2.699 g/cm3
Working in lab = experimental = 2.85 g/cm3
% = 0.055947 100
% = 5.59%
2.699 − 2.85
|100
2.699
2. A student experimentally determines the specific heat of water to be 4.29 J/g x Co. He then looks
up the specific heat of water on a reference table and finds that it is 4.18 J/g x Co. What is the
percent error?
% = |
Reference table = actual = 4.18 J/g x Co
Experimentally determines = experimental = 4.29 J/g x Co
% = 0.026316 100
% = 2.63 %
4.18 − 4.29
|100
4.18
3. A student takes an object with an accepted mass of 200.00 grams and masses it on her own
balance. She records the mass of the object as 196.5 g. What is her percent error?
% = |
Accepted = actual = 200.00 g
% = 0.0175 100
Records the mass = experimental = 196.5 g
% = |
200.00 − 196.5
|100
200.00
% = 1.75 %
4. Often, with accuracy we are concentrating on one measurement. However, we
can also look at a collection of measurements and simply take the average.
Does this target represent someone who is accurate? Yes, because the
average of these points is exactly in the middle of the bulls-eye.
Precise? No, they are not consistent in the least.
CHEMISTRY NOTES – DATA AND MEASUREMENTS